Question

Given 8 cot A = 6. Find sin A and sec A

Answer 1

hello friend....

we have given that:-
8 cot A = 6
=> cot A= 6/8

we have to find
sin A and sec A = ?

now,
we know that:-
sin x = 1/√(1+ cot²x)
&
sec x = 1/√(1-sin²x)
solution:-

sinA = 1/√(1+ cot²A)

= 1/ √{ 1 + (6/8)² }
= 1/ √ (1 + 36/64)
= 1/ √ (64+36)/64
= 1/ √100/64 = 1/ (10/8)= 8/10

now
secA = 1/ √ (1 - sin²A)

= 1/ √ {1 - (8/10)²}
= 1/ √ (1 - 64/100)
= 1/ √ (100-64)/100
= 1/ √ 36/100
= 1/( 6/10 ) = 10/6

hence .
sinA = 8/10
&
secA = 10/6

## Hope it helps##